Name
Abstract | ||
|---|---|---|
This paper presents a volumetric modeling framework to construct a novel spline scheme called restricted trivariate polycube splines (RTP-splines). The RTP-spline aims to generalize both trivariate T-splines and tensor-product B-splines; it uses solid polycube structure as underlying parametric domains and strictly bounds blending functions within such domains. We construct volumetric RTP-splines in a top-down fashion in four steps: 1) Extending the polycube domain to its bounding volume via space filling; 2) building the B-spline volume over the extended domain with restricted boundaries; 3) inserting duplicate knots by adding anchor points and performing local refinement; and 4) removing exterior cells and anchors. Besides local refinement inherited from general T-splines, the RTP-splines have a few attractive properties as follows: 1) They naturally model solid objects with complicated topologies/bifurcations using a one-piece continuous representation without domain trimming/patching/merging. 2) They have guaranteed semistandardness so that the functions and derivatives evaluation is very efficient. 3) Their restricted support regions of blending functions prevent control points from influencing other nearby domain regions that stay opposite to the immediate boundaries. These features are highly desirable for certain applications such as isogeometric analysis. We conduct extensive experiments on converting complicated solid models into RTP-splines, and demonstrate the proposed spline to be a powerful and promising tool for volumetric modeling and other scientific/engineering applications where data sets with multiattributes are prevalent. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/TVCG.2011.102 | IEEE Trans. Vis. Comput. Graph. |
Keywords | Field | DocType |
polycube domain,restricted trivariate polycube splines,domain trimming,volumetric rtp-splines,underlying parametric domain,restricted boundary,local refinement,nearby domain region,extended domain,volumetric data modeling,complicated solid model,model solid object,bounding volume,computational modeling,tensor product,surface reconstruction,solids,spline,surface topography,data model,solid modeling,top down,computer model | Spline (mathematics),Mathematical optimization,Bounding volume,Polycube,Computer science,Isogeometric analysis,Algorithm,Theoretical computer science,Parametric statistics,Solid modeling,Knot (unit),Trimming | Journal |
Volume | Issue | ISSN |
18 | 5 | 1941-0506 |
Citations | PageRank | References |
14 | 0.67 | 16 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kexiang Wang | 1 | 103 | 6.35 |
| Xin Li | 2 | 65 | 10.73 |
| Bo Li | 3 | 71 | 5.73 |
| Huanhuan Xu | 4 | 48 | 2.93 |
| Hong Qin | 5 | 2120 | 184.31 |